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On some commutativity theorems for finite rings and finite groups. (English) Zbl 1050.16018

The relation between nilpotent elements in a ring and commutativity conditions in finite rings and finite groups is investigated.

MSC:

16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16P10 Finite rings and finite-dimensional associative algebras
16N40 Nil and nilpotent radicals, sets, ideals, associative rings
16U80 Generalizations of commutativity (associative rings and algebras)
20F99 Special aspects of infinite or finite groups
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References:

[1] Artin, Emil: Collected Papers. Springer Verlag, 1965. · Zbl 0146.00101
[2] De Morais, Roberto J. F.: On a Representation Theorem for Finite Dimensional Algebras. · Zbl 1050.16018
[3] Jacoboson, Nathan: Collected Mathematical Papers. Birkhäuser, 1989.
[4] Wedderburn, J.H.M.: On hypercomplex numbers. Proc. London Math. Soc. 6 (1908). · JFM 39.0139.01
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